It is common practice to classify defects accordingly to their severity and then to assign each category an acceptable quality level (AQL). How justified is this practice and what guidelines can be given in assigning AQLs? The answer to this depends on how AQL is interpreted. Most generally the AQL is viewed as kind of a cut off point. Lots up to the AQL are acceptable for release. Any lot worse than the AQL should be rejected. This does not mean that all such lots are actually rejected. Often the sampling plan is only capable of rejecting lots significantly above the AQL. However, if a sampling plan rejects a 2% defective lot when the AQL is 1%, no one would consider that an error.
This interpretation of the AQL closely coincides with what is called the break-even quality. The break-even quality is that point where the cost of 100% inspecting a lot is exactly equal to the benefits obtained as a result of fewer defects being released. Lots free of defects (0% defective) are best released. 100% inspecting such lots is a waste of time and money. On the other hand, lots with high levels of defects should be 100% inspected. The cost of the 100% inspection is small compared to the consequences of the defects it eliminates. Somewhere between 0% defective and 100% defective, there is a point where it is a tie. This point is called the break-even quality. Figure 1 shows this point graphically.
Figure 1: Break Even Quality
The break-even quality depends on:
k1 = per unit cost of performing the 100% inspection.
k2 = loss incurred by customer and others as the result of the release of a single defective unit.
The break-even quality (BEQ) is then:
Suppose that the per unit cost of inspection is $0.10 and that each defective released results in an average loss of $10. Then the break-even quality is 1% defective.
If product AQLs are viewed as break-even qualities, then the above formula can be used to establish AQLs. Defects are commonly classified as critical, major, and minors. These categories correspond to differ severity’s, i.e., different values of k2. Within a category, the defects have similar consequences. For example, major defects render the product nonfunctional. The customer is little concerned with why it doesn’t work. The impact is the same. Therefore it makes sense to group these defects together if their inspection costs are similar. In particular, visual defects should be grouped together. Functional defects with higher costs of testing should be inspected separately, not only using a separate sampling plan but also with a higher AQL.
One final note is in order. The AQL is a guide as to what to do with the lot once it is produced. For example, when the AQL is 1%, a 0.5% defective lot is best released. However, it would be better still to have produced a lot free of defects. The AQL should not be viewed as a production goal or as permission to produce defects.
Appeared in FDC Control, Food Drug & Cosmetic Division ASQC, No. 101, Nov. 1993, p. 4
Copyright © 1993 Taylor Enterprises, Inc.
Further information can be found in:
- Book Guide to Acceptance Sampling
- Software package Sampling Plan Analyzer
- STAT-09, Manufacturing Acceptance Sampling Plans and Inspections, of the book Statistical Procedures for the Medical Device Industry